Exact value of the resistance exponent for four dimensional random walk trace
Exact value of the resistance exponent for four dimensional random walk trace
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DOI：
10.1007/s00440-011-0343-x
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发表时间：
2012-06
影响因子：
2
通讯作者：
D. Shiraishi
中科院分区：
文献类型：
--
作者：
D. Shiraishi
设S是一个从原点开始的简单随机游动。我们假设图是整数格的一个随机子图，并假定在图的每一条边上都有一个单位电阻。为原点与Sn之间的有效电阻。我们推导出电阻指数的精确值，更确切地说，我们证明。作为应用，我们得到了猝灭水平上随机游动的精确热核估计.这些结果给出了Burdzy和Lawler（J Phys A Math Gen 23：L23-L28，1990）提出的四维问题的答案。
LetSbe a simple random walk starting at the origin in. We considerto be a random subgraph of the integer lattice and assume that a resistance of unit 1 is put on each edge of the graph. Letbe the effective resistance between the origin andSn. We derive the exact value of the resistance exponent; more precisely, we prove that. As an application, we obtain sharp heat kernel estimates for random walk onat the quenched level. These results give the answer to the problem raised by Burdzy and Lawler (J Phys A Math Gen 23:L23–L28, 1990) in four dimensions.